Ivy is not parasitic, it does not feed off the tree it climbs, but Ivy can over time add so much weight to a tree that it increases the possibility of breaking loose bark. If it is not restricted to the trunk, but has spread out into the canopy, it increases the chance of blow-down in high winds, & especially in stormy areas adds risk. Ivy also increases limb loss in high winds. Ivy heightens these risks by increasing the tree's wind resistance. It is recommendable to remove at least any ivy that climbs away from the trunk, as that which clings to the trunk per se does not increase wind resistance. Ivy that has spread into the canopy can out-compete the tree for sunlight.
Ivy can hide tree-killing infestations, fungus, & diseases that are treatable if spotted in time, but won't be spotted beneath the ivy. Trees that are already ill or near the end of their lives, but which might have had a decade or so of attractive life left in them, may have their time shortened by ivy, by harboring bacterial disease or by providing a haven for increasing numbers of insects, some of which are harmful to trees. Ivy that is doing especially well in a tree can be an early sign that the tree is in decline, & the ivy can hasten the development of disease, but it is not the cause of the sickness.
Hope this helps